How to graph the reciprocal function and identify the characteristics

The video tutorial covers basic trigonometric functions and their transformations, focusing on reciprocal functions. It explains how to identify and shift vertical and horizontal asymptotes, and discusses the domain and range using interval notation. The tutorial also guides students on sketching graphs and finding X and Y intercepts, emphasizing the importance of understanding graph transformations and asymptotes.

What is the effect of subtracting 3 in the denominator of the reciprocal function?

• It shifts the graph 3 units to the left.

• It shifts the graph 3 units to the right.

• It shifts the graph 3 units up.

• It shifts the graph 3 units down.

What happens to the vertical asymptote when the graph is shifted 3 units to the right?

• It shifts to x = 3.

• It shifts to x = -3.

• It remains at x = 0.

• It shifts to x = 1.

What is the domain of the function after the transformation?

• All real numbers except x = 0.

• All real numbers except x = 3.

• All real numbers except y = 0.

• All real numbers except y = 1.

Why is it important to sketch a rough graph?

• To calculate the slope of the graph.

• To visualize the general behavior of the graph.

• To find the exact values of intercepts.

• To determine the exact domain and range.

When does the X intercept occur in a function?

• When x = 1.

• When y = 0.

• When x = 0.

• When y = 1.

What is the Y intercept of the function after transformation?

• y = 1

• y = 0

• y = 3

• y = 2/3

How do you find the Y intercept of a function?

• By setting y = 0 and solving for x.

• By setting x = 0 and solving for y.

• By finding the slope of the function.

• By determining the asymptotes.